Filament propagation

In nonlinear optics, filament propagation is propagation of a beam of light through a medium without diffraction. This is possible because the Kerr effect causes an index of refraction change in the medium, resulting in self-focusing of the beam. Filamentary damage tracks in glass caused by laser pulses were first observed by Michael Hercher in 1964. Filament propagation of laser pulses in the atmosphere was observed in 1994 by Gérard Mourou and his team at University of Michigan. The balance between the self-focusing refraction and self-attenuating diffraction by ionization and rarefaction of a laser beam of terawatt intensities, created by chirped pulse amplification, in the atmosphere creates "filaments" which act as waveguides for the beam thus preventing divergence. Competing theories, that the observed filament was actually an illusion created by an axiconic (bessel) or moving focus instead of a "waveguided" concentration of the optical energy, were put to rest by workers at Los Alamos National Laboratory in 1997. Though sophisticated models have been developed to describe the filamentation process, a model proposed by Akozbek et al. provides a semi-analytical and easy to understand solution for the propagation of strong laser pulses in the air. Filament propagation in a semiconductor medium can also be observed in large aperture vertical cavity surface emitting lasers. A laser beam traversing a medium can modulate the refractive index of medium as where , and are linear refractive index, second order refractive index and intensity of propagating laser field respectively. Self-focusing occurs when the phase shift due to Kerr effect compensates for the phase shift because of Gaussian beam divergence. Phase change due to diffraction for a Gaussian beam after traversing a length of is and phase change because of Kerr effect is where , (Rayleigh range) and is the waist of Gaussian beam. For self-focusing to happen the one have to satisfy the condition of terms be equal in magnitude for both Kerr and diffraction phases.